<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<html>
<head><title>Help - Supervised Wishart Classification</title>


    <link rel="stylesheet" href="../style.css">
</head>
<body>
<table class="header">
    <tbody>
    <tr class="header">
        <td class="header">&nbsp; Supervised Wishart Classification<br>
        </td>
        <td class="header" align="right"><a href="nbdocs://org.esa.snap.snap.help/org/esa/snap/snap/help/docs/general/overview/SnapOverview.html"><img src="../images/snap_header.jpg"
                                                                                 border="0"></a></td>
    </tr>
    </tbody>
</table>
<h3>Supervised Wishart Classification Operator</h3>&nbsp;&nbsp; Terrain
classification is one of the most important applications of
polarimetric synthetic aperture radar. The Supervised Wishart
Classification technique classifies the image into a number of clusters
using Wishart distance measure and user provided training data.
Different from the Unsupervised Wishart Classification, in the
Supervised Wishart Classification the cover types to be classified are
selected by the user. In another word, the clusters (for example,
forest, water and urban) and their locations are known in advance. This
information is provided to the classifier through user selected
training data set. The training set is selected for each class based on
the ground truth map or scattering contrast differences in PolSAR
images. User locates these areas on the image and guide the classifier
with the help of these training sites to learn the relationship between
the data and the classes. Finally, the image pixels are classified into
one of the clusters based on their Wishart distances to the center of the cluster.<br>
<br>
Therefore, this operator consists of two major processing steps:<br>
<ul>
    <li>Supervised Training<br>
    </li>
    <li>Wishart Classification</li>
</ul>
<h4>Supervised Training<br>

</h4>&nbsp;&nbsp; To perform the supervised
training, <span style="font-size: 12pt; font-family: &quot;Times New Roman&quot;;" lang="EN-US"></span>the following
steps should be followed:<br>
<ol>
    <li>Display an intensity image on screen using RSTB (see Figure 1. a subset of RadarSAT-2 data for San Francisco for
        example);<br>
    </li>
    <li>Select areas as training data sets using the "Create a new
        geometry container" and other drawing tools on the right hand side of
        the tool box (in Figure 1, 8 areas for 5 classes have been selected);<br>
    </li>
    <li>Select "Supervised Classification Training" from the
        "Polarimetric" menu, then highlight the training geometries and click
        on "OK" to start the training. The center for the coherency matrices of
        the pixels in each user identified class is computed and save in a text
        file in user specified directory.<br>
    </li>
</ol>

&nbsp;&nbsp; <br>
<img style="width: 453px; height: 566px;" alt="" src="images/supervisedWishartClassificationOp_1.jpg"><br>

<div style="margin-left: 80px;">Figure 1. Training data set: 8 areas for 5 classes<br>

</div>
&nbsp;&nbsp; <br>
Note that this processing step may take some time depending on the
number of classes, the number of areas and the size of the selected
areas.<br>

<h4>Supervised Wishart Classification</h4>
&nbsp;&nbsp; In this processing step, all image pixels are classified to one of the clusters based on their
Wishart distances to cluster centres.<br>
<br>
&nbsp;&nbsp; The cluster centre<span style="font-style: italic;"> V<sub>m</sub></span> for the <span
        style="font-style: italic;">m</span>th cluster is the average of the coherency matrices<sub></sub> of all pixels
in the cluster. Mathematically it is given by <br>

<div style="margin-left: 120px;"><img style="width: 116px; height: 49px;" alt=""
                                      src="images/polarimetricClassification_eq1.jpg"><br>
</div>
<br>
&nbsp;&nbsp; The Wishart distance measure from coherency matrix <span style="font-style: italic;">T</span> to cluster
centre <span style="font-style: italic;">V<sub>m</sub></span> is defined<span
        style="font-size: 12pt; font-family: &quot;Times New Roman&quot;; font-style: italic;"></span><span
        style="font-size: 12pt; font-family: &quot;Times New Roman&quot;; font-style: italic;"></span><span
        style="font-size: 12pt; font-family: &quot;Times New Roman&quot;; font-style: italic;"></span><span
        style="font-size: 12pt; font-family: &quot;Times New Roman&quot;; font-style: italic;"></span><span
        style="font-size: 12pt; font-family: &quot;Times New Roman&quot;;"><span
        style="font-style: italic;"></span></span><span
        style="font-size: 12pt; font-family: &quot;Times New Roman&quot;; font-style: italic;"></span><span
        style="font-style: italic;"></span><span style="font-style: italic;"></span><span
        style="font-style: italic;"></span> as the following:<br>
<br>

<div style="margin-left: 120px;"><img style="width: 204px; height: 35px;" alt=""
                                      src="images/polarimetricClassification_eq2.jpg"><br>
</div>
&nbsp;&nbsp; <br>
&nbsp;&nbsp; where ln() is the natural logarithm function, |.| and
Tr(.) indicate the determinant and the trace of the matrix respectively.<br>
<h4>Input and Output</h4>
<ul>
    <li>The
        input to this operator can be qual-pol data or the coherency / covariance
        matrix generated by Polarimetric Matrix Generation operator.
    </li>
    <li>The
        output of this operator is supervised_wishart_class band with pixel
        values being integers indicating the cluster indices. User can give
        different colour to different cluster by using the RSTB "Colour
        Manipulation" tool. (see Figure 2 for the classification result of the
        example given in Figure 1).
    </li>
</ul>
<ol>
</ol>
<img style="width: 451px; height: 565px;" alt="" src="images/supervisedWishartClassificationOp_2.jpg"><br>

<div style="margin-left: 80px;">Figure 2. Classification result<br>

</div>
<br>

<h4>Parameters Used</h4>
&nbsp;&nbsp; For Supervised training, the following processing parameter are needed (see Figure 3):<br>
<ul>
    <li>Product: the source product</li>
    <li>Training Geometries: user identified classes</li>
    <li>File name: name for the text file in which cluster centers are saved<br>
    </li>

</ul>
<br>
<img style="width: 490px; height: 276px;" alt="" src="images/supervisedWishartClassificationOp_3.jpg"><br>

<div style="text-align: left;">&nbsp;&nbsp;&nbsp;
    &nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;
    &nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp; Figure 3. Dialog box for Supervised training<br></div>
<br><br>
For Supervised Wishart classification, the following parameters are used (see Figure 4):<br>
<ul>
    <li>Training Data Set: the text file in which the computed cluster centers are saved</li>
    <li>Window Size: dimension of sliding window for computing mean covariance or coherency matrix</li>
</ul>
<img style="width: 500px; height: 500px;" alt="" src="images/supervisedWishartClassificationOp_4.jpg"><br><br>&nbsp;&nbsp;&nbsp;
&nbsp;&nbsp;&nbsp;
&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp; Figure 4. Dialog box for Supervised Wishart classification<br>
<br>

<p> Reference:&nbsp;</p>

<p>[1] Jong-Sen Lee and Eric Pottier, Polarimetric Radar Imaging: From Basics to Applications, CRC Press, 2009</p>


<hr>
</body>
</html>